Cont'd Decimal Expansion, rational or not?

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This is a follow up from this question.

Since it's proven by Calvin Lin that $0.11235813213455...$ (Fibonacci Sequence), I'm not wondering if the sequence $$0.123456789101112131415...$$

(which is just natural numbers) is rational or not. Thanks for the help in advanced!

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A number is rational if and only if its decimal expansion terminates or eventually begins repeating. This number does neither.